"I have been lucky," he tells me over the phone from his home in Tehran, "to have had very good reactions from audiences, producers and actors around the globe. But sometimes, people just say, 'This is a linear story of a poor person who lives in Iran and his situation.' I'm like, oh my God, that's not what we're talking about."

It's easy to see why White Rabbit, Red Rabbit has proved such a global hit: it's a tense, entrancing piece of theatre, in which an intrepid performer (everyone from Juliet Stevenson to Sarah Millican has so far squared up to the task) must step on stage with a script he or she has never read before. Written in the playwright's own voice (or a fictional version of that voice, at any rate), the script renders the actor, in effect, a proxy for Soleimanpour; as Soleimanpour, the actor then tells an allegorical story about social conditioning. The key theme is obedience: that of actors and audiences to the conventions of theatre and, by implication, that of the rest of us to society's conventions.

Soleimanpour wrote the play over seven years in his 20s (he's now 33), when he was unable to obtain a passport after refusing to do military service. Many made the assumption that he was critiquing his own country, but his approach to theatre-making is subtler and tricksier than that.

He has long been fascinated by artistic experimentation – his father is a novelist, his mother a painter; growing up, he says, he was rarely able to finish a book before they told him the ending – and at 22 he quit an engineering degree at the University of Tehran in favour of studying drama. He has been able to travel abroad since 2012, when he discovered a disorder in his left eye that exempted him from military service; he is now in touch with experimental theatre-makers around the world, including Canada's Daniel Brooks and Britain's own Tim Crouch.

What excites him are new ways of making and understanding theatre. "When I started writing, I was thinking about when theatre itself became a paradigm. I had this theory that while other schools were trying to experiment with the structure of drama, the Greek school of theatre persisted. I was thinking, who says that we need rehearsals? An actor can just get up and start."

His latest piece, Blind Hamlet – directed by Ramin Gray for the Actors Touring Company – has, along with a fresh run of White Rabbit, Red Rabbit, just opened at the Edinburgh fringe. The play takes his deconstructive approach a step further: it's an interactive game that requires no actors at all. Next up, he says, will be a show that dispenses with a director, actors, rehearsals and set.

It's a wonder he's not getting hate mail from Equity. "Oh, because of Rabbit, many actors are my good friends," he says, laughing. And it seems, anyway, that nothing would sway him from his desire to keep experimenting. "It's a gift. There is no guarantee: you're taking a risk. So I hope I can keep risking my credits, my ideas, my everything."

Blind Hamlet is at the Assembly Roxy, Edinburgh, and White Rabbit, Red Rabbit is at Assembly George Square Studios, both until 25 August. assemblyfestival.com